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"Finally, we thank Sloane for the OEIS [12] which facilitated our making the connection between fence tilings and strongly restricted permutations." [K. Edwards and M. A. Allen, 2015]

"We learned about Lehmer's Theorem 1 via serendipity, thanks to that amazing tool that we are so lucky to have, the On-Line Encyclopedia of Integer Sequences [S] (OEIS). ... the present paper is yet another paper that owes its existence to the OEIS!" [Shalosh B. Ekhad and Doron Zeilberger, 2018]

"For the proof of Lemma 9, the author is indebted to Axel Hultman and Sloane's On-Line Encyclopedia of Integer Sequences." [N. Eriksen, 2005]

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  • Works are arranged in alphabetical order by author's last name.
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References

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  90. Wiktor Ejsmont, Franz Lehner, The Trace Method for Cotangent Sums, arXiv:2002.06052 [math.CA], 2020. (A000032)
  91. Wiktor Ejsmont, Franz Lehner, The Free Tangent Law, arXiv:2004.02679 [math.OA], 2020. (A000828)
  92. Bryan Ek, Lattice Walk Enumeration, arXiv:1803.10920 [math.CO], 2018. (A001764, A002293, A060941, A293946, A300386, A300387, A300388, A300389, A300390, A300391, A300998, A301379, A301380, A301381)
  93. Bryan Ek, Unimodal Polynomials and Lattice Walk Enumeration with Experimental Mathematics, arXiv:1804.05933 [math.CO], 2018. (A000984, A001764, A002293, A002522, A060941, A293946, A300386, A300387, A300388, A300389, A300390, A300391, A300998, A301379, A301380, A301381, A301386, A302612, A302644, A302645, A302646)
  94. Shalosh B. Ekhad, Automated Generation of Anomalous Cancellations, arXiv:1709.03379 [math.HO], 2017.
  95. Shalosh B. Ekhad, Manuel Kauers, Doron Zeilberger, The O(1/n^85) Asymptotic expansion of OEIS sequence A85, arXiv:2410.16334, October 2024.
  96. Shalosh B. Ekhad, Manuel Kauers, and Doron Zeilberger, The O(1/n⁸⁵)$ Asymptotic expansion of OEIS sequence A85, arXiv:2410.16334 [math.CO], 2024. (A000085)
  97. Shalosh B. Ekhad, Christoph Koutschan, and Doron Zeilberger, There are EXACTLY 1493804444499093354916284290188948031229880469556 Ways to Derange a Standard Deck of Cards (ignoring suits) [and many other such useful facts], arXiv:2101.10147 [math.CO], 2021. (A000166, A000459, A059073, A059074, A123297)
  98. Shalosh B. Ekhad, Nathaniel Shar, and Doron Zeilberger, The number of 1...d-avoiding permutations of length d+r for SYMBOLIC d but numeric r, arXiv:1504.02513, 2015.
  99. Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, A Meta-Algorithm for Creating Fast Algorithms for Counting ON Cells in Odd-Rule Cellular Automata, arXiv:1503.01796, 2015.
  100. Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, Odd-Rule Cellular Automata on the Square Grid, arXiv:1503.043249, 2015.
  101. Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, Automated Proof (or Disproof) of Linear Recurrences Satisfied by Pisot Sequences, arXiv:1609.05570, 2016.
  102. Shalosh B. EKHAD and Mingjia YANG, Automated Proofs of Many Conjectured Recurrences in the OEIS made by R.J. Mathar, HTML, July, 2017, arXiv:1707.04654
  103. S. B. Ekhad and D. Zeilberger, Proof of Conway's Lost Cosmological Theorem, Electronic Research Announcements of the Amer. Math. Soc. 3 (1997) 78-82.
  104. Shalosh B. Ekhad and Doron Zeilberger, "There are More Than 2n/17 n-Letter Ternary Square-Free Words", J. Integer Sequences, Volume 1, 1998, Article 98.1.9.
  105. Shalosh B. EKHAD and Doron ZEILBERGER, Automatic Solution of Richard Stanley's Amer. Math. Monthly Problem #11610 and ANY Problem of That Type, Arxiv preprint arXiv:1112.6207, 2011
  106. S. B. Ekhad and D. Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux, Arxiv preprint arXiv:1202.6229, 2012
  107. Shalosh B. EKHAD and Doron ZEILBERGER, Automatic Counting of Tilings of Skinny Plane Regions, Arxiv preprint arXiv:1206.4864, 2012
  108. Shalosh B. Ekhad, Doron Zeilberger, How to generate as many Somos-like miracles as you wish, arXiv:1303.5306
  109. Shalosh B. Ekhad and Doron Zeilberger, Automatic Proofs of Asymptotic Abnormality (and much more!) of Natural Statistics Defined on Catalan-Counted Combinatorial Families, arXiv:1403.5664, 2014.
  110. Shalosh B. Ekhad and Doron Zeilberger, Enumerative Geometrical Genealogy (Or: The Sex Life of Points and Lines), arXiv:1406.5157, 2014.
  111. Shalosh B. Ekhad, Doron Zeilberger, There are (1/30)(r+1)(r+2)(2r+3)(r^2+3r+5) Ways For the Four Teams of a World Cup Group to Each Have r Goals For and r Goals Against [Thanks to the Soccer Analog of Prop. 4.6.19 of Richard Stanley's (Classic!) EC1], arXiv:1407.1919, 2014.
  112. Shalosh B. EKHAD and Doron ZEILBERGER, The Generating Functions Enumerating 12...d-Avoiding Words with r occurrences of each of 1 , . . . , n are D-finite for all d and all r, http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/sloane75.pdf, 2014; also arXiv preprint arXiv:1412.2035, 2014.
  113. S. B. Ekhad, D. Zeilberger, The Method(!) of GUESS and CHECK, arXiv preprint arXiv:1502.04377, 2015.
  114. SB Ekhad and D Zeilberger, Explicit Expressions for the Variance and Higher Moments of the Size of a Simultaneous Core Partition and its Limiting Distribution, arXiv preprint arXiv:1508.07637, 2015.
  115. SB Ekhad and D Zeilberger, Computerizing the Andrews-Fraenkel-Sellers Proofs on the Number of m-ary partitions mod m (and doing MUCH more!), arXiv preprint arXiv:1511.06791, 2015.
  116. SB Ekhad and D Zeilberger, On the number of Singular Vector Tuples of Hyper-Cubical Tensors, arXiv preprint arXiv:1605.00172, 2016.
  117. Shalosh B. Ekhad and Doron Zeilberger, Going Back to Neil Sloane's FIRST LOVE (OEIS Sequence A435): On the Total Heights in Rooted Labeled Trees, arXiv preprint arXiv:1607.05776, 2016.
  118. SB Ekhad, D Zeilberger, A Treatise on Sucker's Bets, arXiv preprint arXiv:1710.10344, 2017.
  119. Shalosh B. Ekhad and Doron Zeilberger, D. H. Lehmer's Tridiagonal determinant: An Etude in (Andrews-Inspired) Experimental Mathematics, arXiv:1808.06730 [math.CO], 2018. (A003116, A039924) We learned about Lehmer's Theorem 1 via serendipity, thanks to that amazing tool that we are so lucky to have, the On-Line Encyclopedia of Integer Sequences [S] (OEIS). ... the present paper is yet another paper that owes its existence to the OEIS!
  120. Shalosh B. Ekhad, Doron Zeilberger, In How many ways can I carry a total of n coins in my two pockets, and have the same amount in both pockets?, arXiv:1901.08172 [math.CO], 2019. (A001971, A001973, A001975, A001977, A001979, A001981, A004526, A323825)
  121. Shalosh B. Ekhad and Doron Zeilberger, Some Remarks on a recent article by J. -P. Allouche, arXiv:1903.09511 [math.CO], 2019. (A006256)
  122. Shalosh B. Ekhad and Doron Zeilberger, Automatic Counting of Restricted Dyck Paths via (Numeric and Symbolic) Dynamic Programming, arXiv:2006.01961 [math.CO], 2020. (A000108, A001006)
  123. Shalosh B. Ekhad and Doron Zeilberger, Automated Generation of Generating Functions Related to Generalized Stern's Diatomic Arrays in the footsteps of Richard Stanley, arXiv:2103.12855 [math.CO], 2021.
  124. Shalosh B. Ekhad and Doron Zeilberger, Some Deep and Original Questions about the "critical exponents" of Generalized Ballot Sequences, arXiv:2104.01731 [math.CO], 2021. (A001006, A001405, A005817, A007578, A007579, A007580, A049401, A126042, A212915, A212916, A229053, A229068)
  125. Shalosh B. EKHAD and Doron ZEILBERGER, Automating John P. D’Angelo’s method to study Complete Polynomial Sequences, Preprint, Nov 2021 [To appear on the arXiv]
  126. Shalosh B. Ekhad and Doron Zeilberger, Counting Clean Words According to the Number of Their Clean Neighbors, arXiv:2304.11253 [math.CO], 2023.
  127. el Houcein el Abdalaoui, Mohamed Dahmoune and Djelloul Ziadi, On the transition reduction problem for finite automata, arXiv preprint arXiv:1301.3751, 2013.
  128. Mohamed El Bachraoui, A Bailey type identity with applications related to integer representations, Proc. Amer. Math. Soc. (2021) Vol. 149, 3187-3200. doi:10.1090/proc/15407
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